#!/usr/bin/perl -w

$hash{"0"} = ["1","2","15"];
$hash{"1"} = ["3","4"];
$hash{"2"} = ["5","6"];
$hash{"3"} = ["7","8"];

# Recursively expand a key in the hash into itself and its values.
# Returns a reference to an array of keys and references to arrays.
# Warning: If $hash{$n} contains $n then this expansion won't 
# terminate.
sub expand {
  my ($key)     = @_;
  my @result = ( $key );                   # Keep the value.
  foreach my $subkey ( @{$hash{$key}} ) {  # If it's a key, expand
    push @result, expand($subkey);         # that too and append.
  }
  return \@result;
}

# Apply the algorithm to find the expanded "0" entry.
$newhash{0} = expand(0) ;

# Pretty print the result as a perl data structure.
use Data::Dumper;
print Dumper( $newhash{0} );

# Like the expand() routine, 
# but keep everything at the same depth.
sub expandFlat {
  my ($key)     = @_;
  my @result = ( $key );                  
  foreach my $subkey ( @{$hash{$key}} ) { 
    push @result, expandFlat($subkey);    
  }
  return @result;
}

# Print out the flattened structure.
print "(". join(",",expandFlat(0))  .")\n";

# Running this and compacting the Data::Dumper output a bit gives
#
# (1)
# As a perl data structure:
# $VAR1 = [ 0, [ '1', [ '3', [ '7' ], 
#                            [ '8' ] ],
#                     [ '4'        ] ],
#              [ '2', [ '5'        ], 
#                     [ '6'        ] ],
#              [ '15'                ] ];
#
# (2) 
# As a flat array
# (0,1,3,7,8,4,2,5,6,15)
#
# which as I said, is pretty much your procedure
# if not quite your outcome.
#